Question
Construct a rectangle $\text{ABCD}$ with perimeter $18\ cm$ and $AB = 6\ cm.$
✓
Answer
Opposite sides of a rectangle are equal.
$\Rightarrow A B=C D$ and $B C=D A$
Perimeter of rectangle $=A B+B C+C D+D A$
$18 \ cm =A B+B C+A B+B C$
$18 \ cm =(6+B C+6+B C)$
$(18-12) \ cm =2 B C$
$B C=3 \ cm$
Therefore, $A B=C D=6 \ cm$ and $B C=D A=3 \ cm$
Steps of construction:
$1)$ Draw a line segment $AB = 6\ cm$
$2)$ On $A$ and $B$ draw perpendiculars $AX$ and $BY$ to $AB$.
$3)$ With $A$ and $B$ as centres and radii $3\ cm$ draw arcs on $AX$ and $BY$.
Mark them as $D$ and $C$ respectively.
$4)$ Join $CD.$
$5)\text{ABCD}$ is the required rectangle.
$\Rightarrow A B=C D$ and $B C=D A$
Perimeter of rectangle $=A B+B C+C D+D A$
$18 \ cm =A B+B C+A B+B C$
$18 \ cm =(6+B C+6+B C)$
$(18-12) \ cm =2 B C$
$B C=3 \ cm$
Therefore, $A B=C D=6 \ cm$ and $B C=D A=3 \ cm$
Steps of construction:
$1)$ Draw a line segment $AB = 6\ cm$
$2)$ On $A$ and $B$ draw perpendiculars $AX$ and $BY$ to $AB$.
$3)$ With $A$ and $B$ as centres and radii $3\ cm$ draw arcs on $AX$ and $BY$.
Mark them as $D$ and $C$ respectively.
$4)$ Join $CD.$
$5)\text{ABCD}$ is the required rectangle.
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